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- W2950859903 abstract "For $Omega_e=(0,e)times (0,1)$ a thin rectangle, we consider minimization of the two-dimensional nonlocal isoperimetric problem given by [ inf_u E^{gamma}_{Omega_e}(u)] where [ E^{gamma}_{Omega_e}(u):= P_{Omega_e}({u(x)=1})+gammaint_{Omega_e}abs{nabla{v}}^2,dx ] and the minimization is taken over competitors $uin BV(Omega_e;{pm 1})$ satisfying a mass constraint $fint_{Omega_e}u=m$ for some $min (-1,1)$. Here $P_{Omega_e}({u(x)=1})$ denotes the perimeter of the set ${u(x)=1}$ in $Omega_e$, $fint$ denotes the integral average and $v$ denotes the solution to the Poisson problem [ -Delta v=u-m;mbox{in};Omega_e,quadnabla vcdot n_{partialOmega_e}=0;mbox{on};partialOmega_e,quadint_{Omega_e}v=0.] We show that a striped pattern is the minimizer for $ell 1$ with the number of stripes growing like $gamma^{1/3}$ as $gammatoinfty.$ We then present generalizations of this result to higher dimensions." @default.
- W2950859903 created "2019-06-27" @default.
- W2950859903 creator A5012994992 @default.
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- W2950859903 date "2013-09-03" @default.
- W2950859903 modified "2023-09-27" @default.
- W2950859903 title "Cascade of minimizers for a nonlocal isoperimetric problem in thin domains" @default.
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